Abstract

Purpose:

Improving accuracy in x-rayimage intensifier (XRII) image distortion correction has clinical impact in order to apply XRII images in a variety of clinical applications more reliably. This study aimed to develop and evaluate a new hybrid mathematic approximation method to correct geometric distortions of XRII images.

Methods:

The proposed hybrid method integrated an MLS (moving least-squares method) and an MBA (multilevel B-spline approximation) approach (MLSMBA). In the hybrid method, MLS is used to generate denser “virtual” data points on the basis of sparse original data points; MBA is applied to approximate an ultimate mapping function based on the generated and original data points. Using both computer-simulated and real XRII images, the authors compared the image distortion correction accuracy of the proposed method with those yielded using a number of previously developed and currently routinely used methods. The comparison methods include the traditional local and global approximation methods, an approach combining both local and global approximation methods, and an author’s previously developed hybrid method by integrating MLS followed by another traditional least-square approximation (MLSILS). The image distortion correction accuracy was evaluated using mean-squared residual errors measured at control and intermediate points. In addition, the impact of pincushion distortion, sigmoidal distortion, local distortion, and control point localization errors on these methods was tested using computer-simulated image data.

Results:

The experimental results using the computer-simulated data showed that unlike the traditional local and global approximation methods that are quite sensitive to pincushion and/or sigmoidal distortion, the MLSMBA method was insensitive to these two types of common distortion depicted in XRII images. Similar to the MLSILS method, sensitivity of MLSMBA to local distortion was lower than or comparable with that of the traditional global approximation method. Although sensitivity of MLSMBA to control point localization errors was higher than that of the global approximation method, as long as the standard deviation of pixel displacement errors was smaller than 0.1 pixels, the overall distortion correction accuracy of MLSMBA remains higher than that of the other methods. By selecting a proper cutoff radius, accuracy of MLSMBA is also higher than that of the other methods (including MLSILS). Experiments on real XRII images yielded similar results. For example, processing results using one XRII image showed that residual error (0.248 ± 0.236 pixels) of MLSMBA was smallest as compared to that of the other methods, including two local approximation methods (0.456 ± 0.352 pixels and 0.370 ± 0.402 pixels), a global approximation method (0.422 ± 0.388 pixels), an approach combining local and global methods (0.389 ± 0.386 pixels), and MLSILS (0.255 ± 0.248 pixels).

Conclusions:

The MLSMBA method could be a better choice to correct geometric distortion of raw XRII images in the following conditions: (1) pincushion distortion, sigmoidal distortion, and local distortion exist simultaneously in the XRII images, (2) the number of original control points (landmarks) is limited, and (3) reusability of the correction mapping function is required.

Received 29 April 2011Revised 07 September 2011Accepted 09 September 2011Published online 14 October 2011

Acknowledgments:

This work was supported by National Natural Science Foundation of China under Grant No. 61003119 and Natural Science Foundation of China under Grant No. 60972122.

Article outline:I. INTRODUCTIONII. MATERIALS AND METHODSII.A. Moving least squaresII.B. Multilevel B-spline approximationII.C. Integration of MLS and MBAII.D. Six other data fitting methodsIII. EXPERIMENTS AND RESULTSIII.A. Computer-based simulationsIII.A.1. Accuracy of MBA in dependence of control lattice sizeIII.A.2. Accuracy of MBA in dependence of data point densityIII.A.3. Dependency of MLSMBA’s accuracy upon density of generated data pointsIII.A.4. Sensitivity of MLSMBA to pincushion and sigmoidal distortionsIII.A.5. Sensitivity of MLSMBA to local distortionIII.A.6. Sensitivity of MLSMBA to control point localization errorsIII.A.7. Overall accuracy of different methodsIII.B. Accuracy on real XRII imagesIV. DISCUSSIONV. CONCLUSIONS